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          算法-堆
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<p><strong>特殊的完全二叉树：</strong> 每层节点都被填满，不过如果最后一层没有填满，就只缺少右边的若干个节点</p>
<p>在<strong>最小堆</strong>中，父节点比它的子节点都要小；在<strong>最大堆</strong>中，父节点比它的子节点大</p>
<ul>
<li>左侧子节点的位置是 2 * index + 1</li>
<li>右侧子节点的位置是 2 * index + 2</li>
<li>父节点的位置是 (index - 1) / 2</li>
</ul>
<h4 id="堆的应用"><a href="#堆的应用" class="headerlink" title="堆的应用"></a>堆的应用</h4><ul>
<li>堆能高效的找到<strong>最大值</strong>和<strong>最小值</strong></li>
<li>找出第 k 个最大（最小）元素</li>
</ul>
<h4 id="第-k-个最大元素图解"><a href="#第-k-个最大元素图解" class="headerlink" title="第 k 个最大元素图解"></a>第 k 个最大元素图解</h4><img src="http://blogs-images.youchen-blog.cn/20200924075228.png" alt="image-20200924075228342" style="zoom:67%;" />

<h4 id="最小堆实现"><a href="#最小堆实现" class="headerlink" title="最小堆实现"></a>最小堆实现</h4><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">MinHeap</span> </span>&#123;</span><br><span class="line">    <span class="keyword">constructor</span>() &#123;</span><br><span class="line">        <span class="built_in">this</span>.heap = [];</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// 交换</span></span><br><span class="line">    swap(i1, i2) &#123;</span><br><span class="line">        <span class="keyword">const</span> temp = <span class="built_in">this</span>.heap[i1]</span><br><span class="line">        <span class="built_in">this</span>.heap[i1] = <span class="built_in">this</span>.heap[i2]</span><br><span class="line">        <span class="built_in">this</span>.heap[i2] = temp</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// 插入</span></span><br><span class="line">    insert(value) &#123;</span><br><span class="line">        <span class="built_in">this</span>.heap.push(value)</span><br><span class="line">        <span class="built_in">this</span>.shiftUp(<span class="built_in">this</span>.heap.length - <span class="number">1</span>)</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// 堆上移</span></span><br><span class="line">    shiftUp(index) &#123;</span><br><span class="line">        <span class="keyword">if</span> (index === <span class="number">0</span>) <span class="keyword">return</span></span><br><span class="line">        <span class="keyword">const</span> parentIndex = <span class="built_in">this</span>.getParentIndex(index)</span><br><span class="line">        <span class="keyword">if</span> (<span class="built_in">this</span>.heap[parentIndex] &gt; <span class="built_in">this</span>.heap[index]) &#123;</span><br><span class="line">            <span class="built_in">this</span>.swap(parentIndex, index);</span><br><span class="line">            <span class="built_in">this</span>.shiftUp(parentIndex)</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// 堆下移</span></span><br><span class="line">    shiftDown(index) &#123;</span><br><span class="line">        <span class="keyword">const</span> leftIndex = <span class="built_in">this</span>.getLeftIndex(index)</span><br><span class="line">        <span class="keyword">const</span> rightIndex = <span class="built_in">this</span>.getRightIndex(index)</span><br><span class="line">        <span class="keyword">if</span>(<span class="built_in">this</span>.heap[leftIndex] &lt; <span class="built_in">this</span>.heap[index])&#123;</span><br><span class="line">            <span class="built_in">this</span>.swap(leftIndex, index)</span><br><span class="line">            <span class="built_in">this</span>.shiftDown(leftIndex)</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">if</span>(<span class="built_in">this</span>.heap[rightIndex] &lt; <span class="built_in">this</span>.heap[index])&#123;</span><br><span class="line">            <span class="built_in">this</span>.swap(rightIndex, index)</span><br><span class="line">            <span class="built_in">this</span>.shiftDown(rightIndex)</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    getParentIndex(i) &#123;</span><br><span class="line">        <span class="keyword">return</span> (i - <span class="number">1</span>) &gt;&gt; <span class="number">2</span></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    getLeftIndex(i) &#123;</span><br><span class="line">        <span class="keyword">return</span> i * <span class="number">2</span> + <span class="number">1</span></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    </span><br><span class="line">    getRightIndex(i) &#123;</span><br><span class="line">        <span class="keyword">return</span> i * <span class="number">2</span> + <span class="number">2</span></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    pop()&#123;</span><br><span class="line">        <span class="built_in">this</span>.heap[<span class="number">0</span>] = <span class="built_in">this</span>.heap.pop()</span><br><span class="line">        <span class="built_in">this</span>.shiftDown(<span class="number">0</span>);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    peek() &#123;</span><br><span class="line">        <span class="keyword">return</span> <span class="built_in">this</span>.heap[<span class="number">0</span>]</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    size() &#123;</span><br><span class="line">        <span class="keyword">return</span> <span class="built_in">this</span>.heap.length</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>


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